Wavelet Frame-Based Fuzzy <i>C</i>-Means Clustering for Segmenting Images on Graphs

In recent years, image processing in a Euclidean domain has been well studied. Practical problems in computer vision and geometric modeling involve image data defined in irregular domains, which can be modeled by huge graphs. In this paper, a wavelet frame-based fuzzy C -means (FCM) algorithm for segmenting images on graphs is presented. To enhance its robustness, images on graphs are first filtered by using spatial information. Since a real image usually exhibits sparse approximation under a tight wavelet frame system, feature spaces of images on graphs can be obtained. Combining the original and filtered feature sets, this paper uses the FCM algorithm for segmentation of images on graphs contaminated by noise of different intensities. Finally, some supporting numerical experiments and comparison with other FCM-related algorithms are provided. Experimental results reported for synthetic and real images on graphs demonstrate that the proposed algorithm is effective and efficient, and has a better ability for segmentation of images on graphs than other improved FCM algorithms existing in the literature. The approach can effectively remove noise and retain feature details of images on graphs. It offers a new avenue for segmenting images in irregular domains.